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Characterization of Hydraulic Parameters via Sensitivity Maps for Frequency‐Based Oscillatory Pumping in 2D, Confined, Weakly Heterogeneous Aquifers.

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Title: Characterization of Hydraulic Parameters via Sensitivity Maps for Frequency‐Based Oscillatory Pumping in 2D, Confined, Weakly Heterogeneous Aquifers.
Authors: Zhu, Jiong, Zha, Yuanyuan, Xu, Dong
Source: Water Resources Research; May2025, Vol. 61 Issue 5, p1-26, 26p
Subject Terms: PARAMETER estimation, RESEARCH personnel, AQUIFERS, TOMOGRAPHY, HETEROGENEITY
Abstract: Multi‐frequency oscillatory pumping, in which the groundwater is extracted during a half period, and then reinjected, has recently been used to characterize aquifer heterogeneity. After the initial transition time, a steady periodic head can be observed at the observation well with constant amplitude and phase shift. However, the efficacy of utilizing multiple frequencies to enhance parameter estimation in hydraulic tomography is debatable. Most studies suggest that using multiple frequencies in joint inversion can gradually improve aquifer imaging. However, some researchers argue that additional frequencies add little to the resolution of hydraulic properties. This raises the question: how much non‐redundant information do multiple frequencies provide? In this study, we derive closed‐form analytical sensitivity maps (i.e., Fréchet kernels) of oscillatory pumping in 2D, unbounded, confined weakly heterogeneous aquifers by the sensitivity equation. It is found that the sensitivity maps of amplitude or phase shift are very similar to the sensitivity of drawdown to hydraulic parameters in constant‐rate pumping. Fréchet kernels indicate that multi‐frequency information, much like multi‐time information, can be instrumental for hydrogeological parameter inversion. According to the Fréchet kernels and their derivatives, we propose a method to select the optimal observation frequency, that is, the distance between the observation well and the pumping well is converted to frequency based on the hydraulic background values. Finally, we compare the effectiveness of single‐frequency and multi‐frequency observations in inverse transmissivity and storativity modeling using the iterative ensemble smoother. The results show that multi‐frequency oscillatory pumping can better characterize aquifer heterogeneity than a single frequency. Plain Language Summary: Hydraulic Tomography (HT) is a method used to characterize the distribution of hydraulic parameters by analyzing how heads respond to pumping at different locations. A newer approach, called Oscillatory Hydraulic Tomography (OHT), uses sinusoidal (wave‐like) pumping instead of constant pumping. Researchers are investigating whether using multiple pumping frequencies in OHT can improve the mapping of hydraulic properties. In this study, we derived and applied Fréchet kernels to understand how sensitive OHT measurements are to changes in hydraulic properties. We found that different frequencies reveal different aspects of hydraulic heterogeneity. Based on this, we developed a strategy to select the most effective frequencies for OHT surveys. Our results show that using multiple frequencies provides valuable, complementary information about heterogeneous parameters. We also explain why some earlier studies reached different conclusions, often due to choosing less effective frequency ranges. Key Points: Sensitivity maps for oscillatory pumping are derived by sensitivity equation for saturated, unbounded, 2D, weakly heterogeneous aquiferThe dependence of sensitivity maps on pumping frequency is revealedMulti‐frequency oscillatory pumping can improve imaging results in the inversion using an iterative ensemble smoother [ABSTRACT FROM AUTHOR]
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Database: Biomedical Index
Description
Abstract:Multi‐frequency oscillatory pumping, in which the groundwater is extracted during a half period, and then reinjected, has recently been used to characterize aquifer heterogeneity. After the initial transition time, a steady periodic head can be observed at the observation well with constant amplitude and phase shift. However, the efficacy of utilizing multiple frequencies to enhance parameter estimation in hydraulic tomography is debatable. Most studies suggest that using multiple frequencies in joint inversion can gradually improve aquifer imaging. However, some researchers argue that additional frequencies add little to the resolution of hydraulic properties. This raises the question: how much non‐redundant information do multiple frequencies provide? In this study, we derive closed‐form analytical sensitivity maps (i.e., Fréchet kernels) of oscillatory pumping in 2D, unbounded, confined weakly heterogeneous aquifers by the sensitivity equation. It is found that the sensitivity maps of amplitude or phase shift are very similar to the sensitivity of drawdown to hydraulic parameters in constant‐rate pumping. Fréchet kernels indicate that multi‐frequency information, much like multi‐time information, can be instrumental for hydrogeological parameter inversion. According to the Fréchet kernels and their derivatives, we propose a method to select the optimal observation frequency, that is, the distance between the observation well and the pumping well is converted to frequency based on the hydraulic background values. Finally, we compare the effectiveness of single‐frequency and multi‐frequency observations in inverse transmissivity and storativity modeling using the iterative ensemble smoother. The results show that multi‐frequency oscillatory pumping can better characterize aquifer heterogeneity than a single frequency. Plain Language Summary: Hydraulic Tomography (HT) is a method used to characterize the distribution of hydraulic parameters by analyzing how heads respond to pumping at different locations. A newer approach, called Oscillatory Hydraulic Tomography (OHT), uses sinusoidal (wave‐like) pumping instead of constant pumping. Researchers are investigating whether using multiple pumping frequencies in OHT can improve the mapping of hydraulic properties. In this study, we derived and applied Fréchet kernels to understand how sensitive OHT measurements are to changes in hydraulic properties. We found that different frequencies reveal different aspects of hydraulic heterogeneity. Based on this, we developed a strategy to select the most effective frequencies for OHT surveys. Our results show that using multiple frequencies provides valuable, complementary information about heterogeneous parameters. We also explain why some earlier studies reached different conclusions, often due to choosing less effective frequency ranges. Key Points: Sensitivity maps for oscillatory pumping are derived by sensitivity equation for saturated, unbounded, 2D, weakly heterogeneous aquiferThe dependence of sensitivity maps on pumping frequency is revealedMulti‐frequency oscillatory pumping can improve imaging results in the inversion using an iterative ensemble smoother [ABSTRACT FROM AUTHOR]
ISSN:00431397
DOI:10.1029/2024WR039157